Figure 3.

Formalization of the optimal subspace hypothesis

(A) Effect of three qualitatively different types of small perturbations of the initial condition (prospectively potent, prospectively readout-null, prospectively dynamic-null) on the three processing stages leading to movement (M1 activity, joint torques, and hand position), as shown in Figure 2A. Unperturbed traces are shown as solid lines, perturbed ones as dashed red lines. Only one example neuron (top) is shown for clarity. Despite all having the same size here (Euclidean norm), these three types of perturbation on the initial state have very different consequences. Left: “prospectively potent” perturbations result in errors at every stage. Middle: “prospectively readout-null” perturbations cause sizable changes in internal network activity but not in the torques. Right: “prospectively dynamic-null” perturbations are inconsequential at all stages.

(B) Time course of the root-mean-square error in M1 activity across neurons and reach conditions, for the three different types of perturbations.

(C) Same as (B) for the root-mean-square error in torques.

(D) The motor potency of the top 20 most potent modes.

In (A)–(C), signals are artificially held constant in the first 100 ms for visualization, and black scale bars denote 200 ms from movement onset. See also Supplemental Math Note S1 and Figure S4.